Half an hour before Lady Gaga is due onstage – and an hour before she actually turns up – the queue outside the Roundhouse stretches away from the venue and a startling distance down Camden High Street. Some of the fans who have turned up to hear the singer debut songs from her forthcoming third album, Artpop, have even gone to the trouble of dressing up as per the instructions she issued on Twitter.

The gig has been dubbed Swinefest after a harrowing new song which, judging by its lengthy and emotional introduction, has its roots in an abusive relationship.

Gaga's instructions began straightforwardly, by suggesting the crowd ape the mermaid outfit she's recently been spotted in, then grew progressively weirder. Where, you wondered, does one source a "bedazzled pig nose" or indeed "paint-coloured dreadlocks for securing 'under the sea' Boticelli-Punk accessories"? Does TK Maxx do "Bowie magician garb"? Finally, she announced that people should come in "clothes you don't mind getting covered in live art".

The gig itself is alternately gripping and slightly maddening. There's something intriguing about the way it deconstructs the standard pop show, with the various costume and wig changes taking place onstage, in front of the crowd. Equally, it's hard not to think she's slightly overselling the album's concept.

She claims it's her dream that "art and pop should come together" as if she's the first person in history to think of linking the two, which research suggests isn't actually the case. Still, she can certainly claim originality in her presentation: the Who, Roxy Music and the Velvet Underground certainly didn't do their stuff while wearing a G-string covered in seashells, dodging stuffed pigs thrown by the crowd.

In addition, for all her lengthy soliloquies about how radical her new material is, you're struck by the creeping sense that it's not that different from the rest of the charts. Swine's continual surges from impassioned piano balladry into electronic noise are striking, but elsewhere are the kind of musical influences that everybody else appears to be influenced by at the moment: Jewels and Drugs offers a plethora of guest appearances from rappers over a grinding dubstep rhythm, and elsewhere there's a hint of gauzy 80s R&B.

But that doesn't mean they're bad songs – Manicure in particular sounds like a huge hit in waiting – and it's hard to pick too many holes in what's happening onstage, which is frequently both ridiculous and ridiculously entertaining. Within minutes of her arrival, she has waved a knife about, feigned a nervous breakdown, been manhandled into a giant cage and hoisted into the air, then laid on the ground kicking her legs in the air, a piece of choreography designed to leave anyone old enough to remember Tiswas thinking wistfully of the show's attempt to launch a dance craze called the Dying Fly.

Later, she sings from within a large, illuminated egg, and engages in a routine with white-clad dancers wearing pig's heads and wielding guns that spray paint over the stage: proof that when it comes to making a mainstream pop gig feel like an event, Lady Gaga really is as far ahead of her peers as she thinks she is.